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In 2000, Nasa conducted an experiment and found that gravity plays an indirect role in flame formation and composition (see the wikipedia article). What role does gravity play? Why does a flame extend in the opposite direction of gravity? Assuming the experiment could be re-created, are there any other forces that would cause a flame to extend beyond a spherical shape?

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The wiki You linked gives the answer! And what do You have in mind about "re-creation" of that experiment? Of course it could! But to which end? The result is known!. –  Georg Mar 2 '11 at 16:06
    
+1. This is a nice question regardless of the wikipedia article. The combustion process will behave in a completely differently manner in a zero gravity environment –  user346 Mar 2 '11 at 16:30
    
@Deepak, You could copy some of the wiki article ande paste here as an answer, couldn't You? –  Georg Mar 2 '11 at 16:38
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@Georg - Yes. Or we could wait for some of the very smart people on this site to have their say. Wikipedia is amazing, yes. But it is hardly the be all and end all of all knowledge. If all of physics.SE got together I'm sure we could substantially improve the quality of physics articles on Wikipedia. –  user346 Mar 2 '11 at 16:41
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Convection causes the flame to be affected by gravity (hot gas is less dense than colder gas and therefore it rises). Without gravity there is no convection, so the mixing of the fuel (vaporized candle wax) and oxidizer happens only by diffusion. Which is a lot slower than convection (so as you can see the flame is a lot less intense) and is also symmetrical (so the flame is spherical, except for where the body of the candle interferes with this).

It might be possible to exert a force on the flame's constituents by using a very strong electric or magnetic field. If this was done in a zero-g environment and if there were differences in the electric charge or magnetic moment of the flame's particles, in principal some effect could be produced. For example if hotter bits were a bit more ionized, they would be affected differently by an electric field than colder bits. In practice I would guess that one would have to choose very carefully the materials used in the flame in order to get an observable effect.

W.r.t. your question, a very small air current directed at the flame would alter its shape (that experiment would have to have been carefully done in very still air).

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